# Kinematics - Acceleration in Two Dimensions. Stuck.

• mattstjean
In summary, the conversation is about someone having trouble with a physics question involving a hockey puck rebounding from a board and determining its average acceleration. They have tried using the cosine law and vector components, but are unable to get the correct answer. They also mention a lawn mower example from the same textbook that they are also struggling with. They are seeking help to understand the concepts and solve the problem correctly.
mattstjean
Hi, I am also having trouble with the hockey puck question.

A hockey puck rebounds from a board as shown in my diagram. The puck is in contact with the board for 2.5 ms. Determine avg acceleration of the puck over the interval.

Vi = 26 m/s Vf = 21 m/s

I tried the cosine law but I keep getting 44 m/s and not 18. I don't understand how you guys got 18 m/s. I've plugged it in at least 100 times as
$v_t = \sqrt{v_1^2 + v_2^2 - 2(v_1)(v_2)cos136} = \sqrt{26^2 + 21^2 - 2(26)(21)cos136} =44 =$

Because that wasn't working I then tried Vector Components and I can't get that to work either. I did:
$V_x = V_B sin \theta + (-V_A cos \beta ) = 21 sin(22) - 26 cos(22) =-16$

and

$V_y = V_B cos \theta + (-V_A sin \beta ) = 21 (cos22) + 26(sin22) = 29$

I then tried to figure out
$\Delta V ^2= \Delta V_x ^2 + \Delta V_y^2 = sqrt{16^2 + 29^2} = 33$

Using that I tried to get the average acceleration by:

$A_av = \Delta V / \Delta T A_av = 33 / 2.5x10^-3 A_av = 13.2x10^3$
and to find the angle I tried to do :

$\phi = tan^-1 = 16/29 \phi = 29degrees$

However, the answer in my book says that the average acceleration is $7.3x10^3 [7.5degrees North of West]$
Any help would be amazingly appreciated. Thanks.

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mattstjean said:
Because that wasn't working I then tried Vector Components and I can't get that to work either. I did:
$V_x = V_B sin \theta + (-V_A cos \beta ) = 21 sin(22) - 26 cos(22) =-16$
You have a mix of sine and cosine. Only one is correct.
and

$V_y = V_B cos \theta + (-V_A sin \beta ) = 21 (cos22) + 26(sin22) = 29$
Again, a mix of sine and cosine.

Redo this.

Doc Al said:
You have a mix of sine and cosine. Only one is correct.

Again, a mix of sine and cosine.

Redo this.

I don't know how to redo it. In my textbook it used them both together in the y and x component vector subtraction. I took the equations right out of my text, Nelson Physics 12.

mattstjean said:
I don't know how to redo it. In my textbook it used them both together in the y and x component vector subtraction. I took the equations right out of my text, Nelson Physics 12.
I'm not sure what equations you are talking about.

Do this: What's the x-component of Vi? The x-component of Vf?

I have the same book and I am stuck on the example on right before the quesion box you asked about. can you please explain the lawn mower example in pg 28. I AM VERY CONFUSED

## 1. What is kinematics?

Kinematics is the branch of physics that studies the motion of objects without considering the forces that cause the motion.

## 2. What is acceleration in two dimensions?

Acceleration in two dimensions refers to the change in velocity of an object in two different directions, typically represented by the x and y axes.

## 3. How is acceleration in two dimensions calculated?

Acceleration in two dimensions is calculated by dividing the change in velocity in each direction by the change in time.

## 4. What are some examples of two-dimensional acceleration?

Some examples of two-dimensional acceleration include a ball rolling down a ramp, a plane taking off or landing, and a car making a turn.

## 5. How does acceleration in two dimensions differ from one-dimensional acceleration?

In one-dimensional acceleration, the object is only moving in one direction, so the acceleration is only measured in that direction. In two-dimensional acceleration, the object is moving in two directions, so the acceleration must be calculated for each direction separately.

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